Sashi can do a piece of work in 20 days. Tanya is 25 percent more efficient than Sashi. How many days will Tanya alone take to complete the same work?

Introduction / Context:
This question deals with comparative efficiency. We are told that one worker is 25 percent more efficient than another and given the time taken by the less efficient worker. The aim is to find how long the more efficient worker will take to complete the same job alone.

Given Data / Assumptions:

• Sashi can complete the work in 20 days.
• Tanya is 25 percent more efficient than Sashi.
• Both maintain a constant working rate.
• We must determine the time required by Tanya alone to complete the entire work.

Concept / Approach:
If Tanya is 25 percent more efficient, her work rate is 1.25 times the work rate of Sashi. Efficiency is directly proportional to work rate and inversely proportional to the time needed for the job. Therefore, if the work rate increases by a factor, the time taken decreases by the same factor. We first calculate Tanya's rate as a multiple of Sashi's rate and then obtain her time as total work divided by her rate.

Step-by-Step Solution:
Step 1: Let the total work be 1 unit.Step 2: Sashi completes the work in 20 days, so Sashi's rate = 1 / 20 of the work per day.Step 3: Tanya is 25 percent more efficient than Sashi. This means Tanya's rate = 1.25 times Sashi's rate = 1.25 * (1 / 20).Step 4: Convert 1.25 to fraction 5 / 4. So Tanya's rate = (5 / 4) * (1 / 20) = 5 / 80 = 1 / 16 of the work per day.Step 5: Time taken by Tanya alone = 1 divided by her rate = 1 / (1 / 16) = 16 days.

Verification / Alternative check:
We can compare the times directly using the efficiency ratio. If Sashi takes 20 days, and Tanya is 1.25 times as efficient, Tanya should take 20 / 1.25 days. Compute 20 / 1.25 = 20 * (4 / 5) = 16, which matches the rate based calculation. This confirms that 16 days is correct.

Why Other Options Are Wrong:

• 15 days: This would imply a work rate greater than 1 / 16 and therefore an efficiency gain larger than 25 percent.
• 18 days: This corresponds to a rate of 1 / 18, which is less efficient than 1 / 16, so it does not match the stated 25 percent increase.
• 25 days: This is longer than Sashi's time, which contradicts Tanya being more efficient.

Common Pitfalls:
Some students treat 25 percent more efficient as meaning Tanya's time is 25 percent less and then subtract 25 percent of 20 from 20 without checking the correct factor, which would give 15 days. While this sometimes works, it can lead to confusion. It is safer to work through rates and use multiplicative factors, especially for more complicated percentage changes.

Final Answer:
Tanya alone will take 16 days to complete the work.